Numerical Studies of Wall Effects of Laminar Flames

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Numerical Studies of Wall Effects

of Laminar Flames

Johan Andrae

Licentiate of Engineering Thesis

Royal Institute of Technology

Department of Chemical Engineering and Technology

Chemical Reaction Engineering

Stockholm 2001

TRITA-KET R145

ISSN 1104-3466

ISRN KTH/KET/R--145--SE

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Abstract

Numerical simulations have been done with the CHEMKIN software to study different aspects of wall effects in the combustion of lean, laminar and premixed flames in an axisymmetric boundary-layer flow.

The importance of the chemical wall effects compared to the thermal wall effects caused by the development of the thermal and velocity boundary layer has been investigated in the reaction zone by using different wall boundary conditions, wall temperatures and fuel/air ratios. Surface mechanisms include a catalytic surface (Platinum), a surface that promotes recombination of active intermediates and a completely inert wall with no species and reactions as the simplest possible boundary condition.

When hydrogen is the model fuel, the analysis of the results show that for atmospheric pressure and a wall temperature of 600 K, the surface chemistry gives significant wall effects at the richer combustion case (φ=0.5), while the thermal and velocity boundary layer gives rather small effects. For the leaner combustion case (φ=0.1) the thermal and velocity boundary layer gives more significant wall effects, while surface chemistry gives less significant wall effects compared to the other case.

For methane as model fuel, the thermal and velocity boundary layer gives significant wall effects at the lower wall temperature (600 K), while surface chemistry gives rather small effects. The wall can then be modelled as chemically inert for the lean mixtures used (φ=0.2 and 0.4). For the higher wall temperature (1200 K) the surface chemistry gives significant wall effects.

For both model fuels, the catalytic wall unexpectedly retards homogeneous combustion of the fuel more than the wall that acts like a sink for active intermediates. This is due to product inhibition by catalytic combustion. For hydrogen this occurs at atmospheric pressure, but for methane only at the higher wall temperature (1200 K) and the higher pressure (10 atm).

As expected, the overall wall effects (i.e. a lower conversion) were more pronounced for the leaner fuel-air ratios and at the lower wall temperatures.

To estimate a possible discrepancy in flame position as a result of neglecting the axial diffusion in the boundary layer assumption, calculations have been performed with PREMIX, also a part of the CHEMKIN software. With PREMIX, where axial diffusion is considered, steady, laminar, one-dimensional premixed flames can be modelled. Results obtained with the same initial conditions as in the boundary layer calculations show that for the richer mixtures at atmospheric pressure the axial diffusion generally has a strong impact on the flame position, but in the other cases the axial diffusion may be neglected.

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Sammanfattning

Numeriska simuleringar har gjorts med program i CHEMKIN-paketet för att undersöka olika aspekter av väggeffekter vid förbränning av magra, laminära och förblandade flammor i en axisymmtrisk gränskiktsströmning.

Betydelsen av de kemiska väggefekterna jämfört med de termiska väggeffekterna (utvecklingen av temperatur och hastighetsgränskiktet) har undersökts i reaktionszonen genom att använda olika väggmaterial , väggtemperaturer och bränsle/luft-förhållanden. Ytmekanismer inkluderar en katalytisk yta (Platina), en yta som rekombinerar aktiva intermediärer, och som enklaste randvillkor används en helt inert vägg utan några species eller reaktioner.

Vid analys av resultaten när väte används som modellbränsle vid atmosfärstryck och en väggtemperatur på 600 K, kan ses att de kemiska väggeffekterna är betydande vid det feta bränsle/luft-förhållandet (φ=0.5), medan de termiska väggeffekterna ger ganska små effekter. Vid det magra bränsle/luft-förhållandet (φ=0.1) är de termiska väggeffekterna mer betydande, medan de kemiska väggeffekterna är mindre betydande jämfört med det andra fallet.

När metan används som modellbränsle är de termiska väggeffekterna betydande vid den lägre väggtemperaturen (600 K) medan de kemiska väggeffekterna ger små effekter. Väggen kan då modelleras som kemiskt inert vid de använda bränsle/luft förhållandena (φ=0.2 och 0.4). Vid den höga väggtemperaturen (1200 K) är de kemiska väggeffekterna betydande. För både väte och metan, retarderar den katalytiska väggen oväntat den homogena förbränningen av bränslet mer än väggen som rekombinerar aktiva intermediärer. Orsaken är produktinhibering genom katalytisk förbränning. För väte inträffar detta vid atmosfärstryck, men för metan bara vid den högre väggtemperaturen (1200 K) och det höga trycket (10 atm). Som väntat är de totala väggeffekterna mer betydande (lägre omsättning av bränslet) vid de magra bränsle luft/förhållandena och de lägre väggtemperaturerna.

För att uppskatta en möjlig avvikelse i positionen av flamman (reaktionszonen) som en konsekvens av att den axiella diffusionen försummas i gränskiktsantagandet, har beräkningar gjorts med PREMIX, som är en del av CHEMKIN-paketet. Med PREMIX, där den axiella diffusionen ingår, kan endimensionella, stationära, laminära förblandade flammor modelleras. Resultat för samma initialvillkor som i gränsskikts-beräkningarna indikerar att vid de feta bränsle/luft förhållandena och atmosfärstryck har den axiella diffusionen en stor inverkan på flampositionen, men i övriga fall kan den axiella diffusionen försummas.

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List of Publications

The work presented in this thesis is based on the following publications:

I. Andrae, J., and P. Björnbom, ”Wall Effects of Laminar Hydrogen Flames over Platinum and Inert Surfaces,” AIChE J., 46(7), 1454 (2000).

II. Andrae, J., P. Björnbom, and L. Edsberg, ”Numerical Studies of Wall Effects of Laminar Methane Flames,” submitted to Combust. Flame (2001).

Conference/symposia contributions:

Andrae, J., and P. Björnbom, ”Numerical Investigation of Wall Effects for Laminar Hydrogen Flames over Platinum and Inert Surfaces,” Oral Presentation, Combustion Reaction Engineering, Paper 289j, AIChE Annual Meeting, Dallas, Texas, USA, Oct. 31-Nov. 5 (1999)

Andrae, J., P. Björnbom, and L. Edsberg, ”Numerical Studies of Laminar Methane Flames in a Boundary Layer,” Work in Progress Poster, Laminar Models (Paper 5-A02), Twenty-Eighth

Symposium (International) on Combustion, Edinburgh, Scotland, July 30-Aug. 4 (2000).

Björnbom, P., Andrae, J., Edsberg, L, and D. Papadias, ”Modeling the Kinetics of Catalytic Monolith Reactors,” Invited Plenar Lecture, Proceedings of the Ninth International

Symposium on Heterogeneous Catalysis, Eds. L. Petrov, Ch. Bonev, and G. Kadinov, Varna,

Bulgaria, Sept. 23-27, p. 3 (2000).

Andrae, J., P. Björnbom, and L. Edsberg, ”Modeling Wall Effects of Laminar Methane Flames in a Boundary Layer,” Poster Presentation, Kinetics, Catalysis and Reaction

Engineering, Paper 361x, AIChE Annual Meeting, Los Angeles, California, USA, Nov. 12-17 (2000).

Andrae, J., P. Björnbom, and L. Edsberg, ”Numerical Studies of Wall Effects of Laminar Methane Flames,” Proceedings of the First Biennial Meeting of the Scandinavian-Nordic

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Combustion of fossil fuels is the most important energy source in the world today. About 90% of the worldwide energy production was provided by combustion in 1997. Combustion is used for transportation, electrical power generation, heating and process engineering. The strong dominance of combustion will continue in the foreseeable future, at the same time the world energy production is projected to increase by 60% in the next 20 years (Energy Information Administration, 2000).

Combustion has a major impact on the global environment through the emissions of CO2,

which is the greenhouse gas. Emissions of NOx, SOx, PAHs, CO and particles lead to

decreased air quality, acid rain and health hazards. Because combustion systems are so widespread it is important to improve their efficiency and decrease their negative impact on the environment. These improvements in efficiency and decreases in pollutant formation of combustion systems are only possible through an improved understanding of the fundamental processes taking place during combustion.

The interaction between combustible gases and surfaces is important in determining emissions from a system. Excess emissions of unburned hydrocarbons in combustion engines have long been attributed to the presence of cool walls (Daniel, 1956; Westbrook et al, 1981, Kiehne et al, 1986; Hocks et al, 1981; Sloane and Schoene, 1983). The trend to more usage of lean combustion, for example in novel spark ignition engines, has made wall effects even more significant. A main advantage with these new engines is the ultra-lean mixtures that are used. The combustion is said to be stoichiometric if the amount of oxygen in the premixed fuel-air mixture is enough to oxidize the fuel to CO2 and H2O, and the combustion is said to

be lean if there is an excess of oxygen in the premixed fuel-air mixture, which will give unreacted O2 after reaction. If less oxygen than stoichiometric is used the combustion is rich.

The mole fraction of the fuel in a stoichiometric mixture with air is

xfuel,stoich = 1/ (1 + ν ⋅ 4.762) (1)

where ν denotes the mole number of O2 in the reaction equation for a complete reaction to

CO2 and H2O. An example is CH4 + 2 O2 → CO2 + 2 H2O which gives xfuel,stoich = 9.5

mole-%. Premixtures of fuel and air are characterized by the fuel equivalence ratio

φ = (xfuel/xair)/(xfuel,stoich/xair,stoich) (2)

where x is the mole fraction. This is the ratio of the actual fuel-air ratio to the stoichiometric fuel-air ratio. For example φ = 1 is equal to stoichiometric combustion and φ = 0.5 is equal to an air-excess of 100%. Lean combustion reduces the flame temperature, the fuel consumption and the emission of carbon dioxide. The reduction of fuel consumption in cars is currently one of the most demanding issues in the World from the point of reducing CO2 in

the atmosphere. In traditional spark ignition engines stoichiometric mixtures of fuel and air are burned. This gives a high flame temperature, and the heat from the flame is sufficient to reduce the negative effects from the cold cylinder wall. However when the lean mixtures are burned in novel spark ignition engines, the effects from the cooled wall can be significant. Due to the stratification of the fuel/air mixture and the concentration of the fuel close to the spark plug there will be even leaner conditions in other parts of the cylinder.

In the direct vicinity of the cold walls flame propagation is quenched due to radical depletion in the cold near wall zone by recombination. The radicals can also diffuse to the wall and be heterogeneously quenched. Some of the fuel in the fuel/air mixture left unburned at the wall

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can be transported from the boundary layer to the main flow of the flame gases by diffusion and be oxidized. The remaining fuel may be discharged into the exhaust gases as residual hydrocarbon emissions.

In addition, the treatment of the exhaust gas by catalytic conversion does not work well with lean-burn combustion because the molecules in the exhaust gas do not "add up" like in the three-way-catalyst-concept in traditional engines. The oxygen consumes the reduction matter, normally unburned hydrocarbons from the main flow, and there is not enough to reduce all nitrogen oxides. Lean-burn engines therefore have difficulties to match the output levels of HC, NOx and CO compared to the three-way-catalyst engines. The challenge will be to find a

catalyst that can selectively reduce the NOx to N2 in the presence of some reduction matter.

A novel concept is also Homogeneous Charge Compression Ignition-engines (HCCI). In these internal combustion engines no flame combustion takes place. Very lean mixtures are used, and the bulk mixture self-ignites due to the high pressures used in the cylinders. Due to the low temperatures as a result of the lean mixtures burned, very low NOx and particulate

emission levels are achieved. But the wall effects can be significant and the result is unburned hydrocarbons and CO emissions.

The effect from the combustor wall is also an important issue in lean-burn gas turbines for energy production, for example the burnout of CO in a cooled boundary layer flow (Correa, 1992). In opposite to the spark-ignition engine, the wall temperature is several hundred degrees higher and the process is stationary. The wall effects that arise in a lean-burn gas turbine combustor can therefore be expected to differ from those in a lean-burn spark ignition engine.

Gaining deeper understanding into the physics controlling emissions related to flame-surface interactions are important, especially for lean-burn devices, but is currently not so well understood. Complicating effects in the spark-ignition engine are unsteady boundary layers and piston induced fluid motion (Popp and Baum, 1997).

Numerical simulation offers an interesting alternative method to experiments for the investigation of near-wall combustion. To this end, as the problem is very complex, a fundamental knowledge of the wall effects can be gained by performing numerical simulations where the underlying flow field is laminar. Although the chemical reactions in both an internal combustion engine and in a gas turbine take place in a turbulent flow field, there will always be a laminar sub-layer close to the wall. This suggests that results obtained for laminar flow fields may also be valid, to a certain extent, in the case of turbulent flow conditions. In turbulent flows, the mixing between the fuel and the oxidant is drastically enhanced and in general the heat- and mass-transfer rates would be higher in a turbulent boundary layer than in a laminar boundary layer. This should enhance wall effects in the case of turbulent boundary layers as opposed to laminar ones. In a later stage, the modeling results obtained for laminar flow can be compared with results of calculations done on turbulent reacting boundary layers using computational fluid dynamics (CFD).

This thesis describes the numerical modeling work done with software in the CHEMKIN collection (Kee et al., 1999) to get a fundamental knowledge of wall effects of steady, laminar, and premixed flames in a boundary layer flow. Model fuels have been hydrogen and methane.

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The CHEMKIN software is one of the most successful and enduring products coming out from Sandia National Laboratories in the United States. The software is a powerful tool for solving complex chemical kinetic problems and incorporating this information into simulations of reactive flows. Using CHEMKIN, the researcher is able to investigate thousands of reaction combinations to develop a comprehensive understanding of a particular process, which might involve numerous chemical species, disparate concentration ranges, and a large range of gas temperatures. At Sandia, CHEMKIN is used extensively in the Combustion Research Facility’s modeling work, in chemical vapor deposition studies, and in fire simulations for nuclear weapons programs.

CHEMKIN arose out of Sandia’s combustion research, which began at the Livermore, CA site in the aftermath of the 1970’s oil crisis. Combustion research entails a wide variety of problems involving complex chemical interactions, and researchers needed a general-purpose kinetics simulator to support theoretical modeling studies. CHEMKIN was born. A homegrown effort, the CHEMKIN family of software grew as researchers’ needs and interests evolved. Capabilities in molecular transport, chemistry at deposition surfaces, and plasma processes gradually were added to the initial core software. Because Combustion Research Facility’s scientists and engineers collaborate extensively with colleagues in industry and academia, word spread of the software and requests for it grew. By the mid-1990s, more than a thousand copies of CHEMKIN were in circulation worldwide. Recognizing the value of the software and the need for technical support and development, Sandia licensed CHEMKIN to Reaction Design in February 1997. The CHEMKIN collection today is composed of building blocks that can be applied to a wide range of reacting flow problems. In its 20-old years of existence, CHEMKIN has enabled significant strides in the modeling of complex chemical processes such as combustion. It has become the standard for anyone involved in chemistry modeling and chemically reacting flow modeling.

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3 Numerical modeling of wall effects

Wall effects in combustion are a complicated problem to analyze since many species and still more reactions are involved. The most complex situation is encountered when chemical interactions are established between the gas and the wall such as in catalytic combustion. The

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simplest possible situation is of a chemically “inert” wall in which the coupling between the gas and the wall is mainly of a thermal nature. There are no completely inert walls though, and active radical destruction must also be considered a possibility. To make quantitative predictions, calculations with rigorous fluid mechanics and transport coefficients are necessary. It is inadequate to use global chemistry as it does not account for the role of the radical pool (see section 4.1.1) and also the intermediate hydrocarbons are significant during quenching and must be accounted for in the reaction schemes (Hocks et al., 1981; Kiehne et al., 1986; Hasse et al., 2000). Although lean combustion of simpler hydrocarbons like methane have limited pathways of forming intermediate hydrocarbons, detailed chemistry schemes are necessary to describe the interaction between transport and fuel oxidation in the gas and on the surface. The results are further improved if the effect of thermal diffusion (Soret effect) is considered (Popp and Baum, 1997). Thermal diffusion is the diffusion of mass caused by temperature gradients. The simplest of the catalytic systems, combustion of hydrogen over Platinum, is now sufficiently well understood that some of the problems can be analyzed (such as Bui et al., 1996; Park et al., 1999a).

Fig. 1 Typical flow configurations used to model Flame-Wall interaction (Cleary and Farrel, 1995).

To model the flame-wall interaction, two geometries are often used: the stagnation point flow and the boundary (i.e. sidewall) layer flow where the flame interacts with the wall parallel and perpendicular respectively (Cleary and Farrel, 1995). This is illustrated in Fig. 1. To model the sidewall configuration, in this work the program CRESLAF has been used (Coltrin et al., 1993). CRESLAF is an acronym for Chemically Reacting Shear Layer Flow and is a part of the CHEMKIN collection (Kee et al., 1999).

3.1 Description of CRESLAF

With the CRESLAF program, laminar, chemically reacting boundary-layer flow in two-dimensional planar or axisymmetric channels can be modeled. The program accounts for finite-rate gas-phase and surface chemical kinetics and molecular transport. The model employs the boundary-layer approximations, i.e. the Navier-Stokes equations can be reduced to a system of parabolic partial differential equations describing the conservation of mass,

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momentum, energy, and species composition. The approximation relies on the existence of a principal flow direction in which convective transport is dominant and diffusive effects are negliable (see section 6). For a planar configuration the conservation equations can be written as Momentum: . g u u u x d p d x u u ρ ρ µ ρ ρ _+      Ψ ∂ ∂ Ψ ∂ ∂ = + ∂ ∂ ₍₃₎ Thermal energy: Ψ ∂ ∂ ∑ − ∑ −       Ψ ∂ ∂ Ψ ∂ ∂ = ∂ ∂ = = T V Y c u h M T u u x T c u K _ky k pk k k k K k k p g g 1 2 1 . ρ ω λ ρ ρ ρ . (4) Species:

(

)

, 1,,, 1 . − = Ψ ∂ ∂ − = ∂ ∂ g ky k k k k _M _u _Y _V _k _K x Y u ω ρ ρ ρ . (5) Equation of state: ∑ = = g K k k k M Y RT p 1 ρ . (6) Surface species: s k k s _k _K dt dZ , , , , 1 . = Γ = . (7)

In the above expressions ρ= the mass density, c_p= mixture specific heat capacity, M_k= molecular mass of species k, hk= specific enthalpy, µ= viscosity, λ= thermal conductivity,

p= thermodynamic pressure, R= universal gas constant, V_ky= multicomponent diffusion velocities in the radial direction (including thermal diffusion), k

.

ω = chemical production rate by gas phase reaction, sk

.

= chemical production rate of species by surface reaction, K_g= number of gas phase species, Ks= number of surface species, u= axial velocity, T =

temperature, Yk= gas-phase species mass fractions, Zk= the surface species site fractions and

Γ= surface site density.

The independent variables are x, the distance along the channel, and Ψ=∫₀yρudy, a density-weighted stream function coordinate normal to the surface, where y is the physical space coordinate normal to the surface. This transformation has been done to somewhat simplify the numerical procedure. The dependent variables in this parabolic differential equation system arep,ρ,u,T,Y_k, and Zk. CRESLAF is designed to solve the stationary problem and Eq. (7)

simply states that a steady state the surface composition does not change. In some sense it could be considered a (possible complex) boundary condition on the gas-phase system.

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However, because the surface composition is determined as a part of the solution, Eq. (7) should be considered a part of the system of governing equations. The surface boundary condition becomes relatively complex in the presence of heterogeneous surface reactions. The convective and diffusive mass fluxes of gas-phase species at the surface are balanced by the production (or depletion) rates of gas-phase species by surface reactions, i.e.

k k ky k k Y V u s M j =ρ ( + )= . , k=1,,,K_g (8)

where uis the so-called Stefan velocity, which occurs when there is a net mass flux between the gas and the surface. The detailed mathematical description of the model is given by Coltrin et al. (1986). The boundary layer equations are cast as a system of differential/algebraic equations by the method-of-lines approach. The resulting system of differential/algebraic equations in x is solved using the DASSL software (Brenan et al., 1996). DASSL solves the equations in marching fashion, starting from the inflow (x = 0). CRESLAF runs in conjunction with the CHEMKIN (Kee et al., 1996), SURFACE CHEMKIN (Coltrin et al., 1996) and TRANSPORT (Kee et al., 1986) software packages of Fortran subroutines. The CHEMKIN package is used to calculate the homogeneous reaction rates of the gas-phase species as well as handle thermodynamic data for the system (Kee et al., 1990), the SURFACE CHEMKIN package to formulate the boundary conditions describing chemical reactions at the surface and the TRANSPORT package for calculating the multicomponent diffusivities (including thermal diffusion coefficients), thermal conductivities and viscosities. Data on the thermochemistry of the chemical species are needed in order to calculate reverse rate constants for the chemical reactions. When CRESLAF executes, it reads the linking-file information from the three pre-processors, and makes calls to the subroutine libraries using this linking data.

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4 Hydrogen as model fuel (I)

In the first investigation hydrogen was the model fuel. Previous studies on wall effects had most commonly used the stagnation configuration (such as Popp and Baum, 1997; Aghalayam et al., 1998). Therefore, the aim of this study was to investigate the wall effects of stationary H2 flames with CRESLAF in a two-dimensional sidewall configuration, and especially the

thermal and kinetic effects the cooled wall gave rise to. Different wall boundary conditions and gas-phase transport parameters were used in order to address questions such as which part of the wall effects was most important at a given set of conditions. Hydrogen is a

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hydrocarbon and as fewer reactions and species are involved compared to more complex fuels, the interpretation of the results is easier. On the other hand, as hydrogen is a non-hydrocarbon, the results obtained may not be true for fuels like methane and propane.

4.1 Chemical kinetics models

4.1.1 Gas-phase chemistry

The kinetics of the gas phase reactions for hydrogen oxidation is very well established. Its validity has been established through numerous studies of flames and different reactor types. Even if some details in the reaction mechanism have been changed throughout the years, the basic concept is still valid. The mechanism used in this work was taken from a work with detailed chemistry (Giovangigli and Smooke, 1987) and is shown in Table 1. The three numbers after each reaction corresponds to the three Arrhenius parametersA, nand Ein the expression n ( E RT)

f AT e

k = − / in unit cm3/(mol⋅s). The activation energies are given in the unit kJ/mole. Reverse reaction rates are calculated from forward coefficients and equilibrium constants. The equilibrium constants are calculated from the thermodynamic properties of the species.

The combustion of H2 in air proceeds through a chained branched explosion if a fuel-air

mixture within the flammability limits (the leanest or richest concentrations that will self-support a flame) comes in contact with an ignition source (Glassman, 1996a). Chain branched explosions are characterized by an ignition delay time, where the radical pool is built up (Warnatz et al., 1996b). This means that during the first phase of the explosion the temperature will not increase that much, because the energy released from the fuel and the oxidizer is stored in the free radicals. With time the radical concentration increases and either the fuel or the oxidizer concentration gets low. At that time radical recombination or chain termination reactions become faster than chain-branching reactions and the energy is finally released.

The radical concentrations decrease and the temperature increase until the thermodynamic equilibrium of the system is finally reached. Examples of the different types of chain reactions in the reaction mechanism in Table 1 are: Initiation (No. 5, forward reaction), Chain-branching (No. 1, forward reaction), Propagation (No. 2, 3 & 4 forward reactions) and Termination (No. 8, backward reaction).

Table 1. Gas Phase Reaction Mechanism for Hydrogen-Air (CHEMKIN format). Source: V.Giovangigli and M.D Smooke, Comb. Sci. Tech., 1987.

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ELEMENTS O H PT N END !N/HE

SPECIES O O2 H H2 OH HO2 H2O H2O2 N2 END REACTIONS KJOULES/MOLE

H+O2 = O+OH 5.1E16 -0.82 69.1 !1 H2+O = H+OH 1.8E10 1.0 37.0 !2 H2+OH = H2O+H 1.2E09 1.3 15.2 !3

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OH+OH = H2O+O 6.0E08 1.3 0.0 !4 H2+O2 = OH+OH 1.7E13 0.0 200 !5 H+OH+M = H2O+M 7.5E23 -2.6 0.0 !6 H2O /20.0/

O2+M = O+O+M 1.9E11 0.5 400.1 !7 H2+M = H+H+M 2.2E12 0.5 387.7 !8 H2O /6.0/

H /2.0/ H2 /3.0/

H+O2+M = HO2+M 2.1E18 -1.0 0.0 !9 H2O /21.0/

H2 /3.3/ O2 /0.0/

N2 /0.0/ ! HE/N2

H+O2+O2 = HO2+O2 6.7E19 -1.42 0.0 !10

H+O2+N2 = HO2+N2 6.7E19 -1.42 0.0 !11 HE/N2 HO2+H = H2+O2 2.5E13 0.0 2.9 !12

HO2+H = OH+OH 2.5E14 0.0 7.9 !13 HO2+O = OH+O2 4.8E13 0.0 4.2 !14 HO2+OH = H2O+O2 5.0E13 0.0 4.2 !15 HO2+HO2 = H2O2+O2 2.0E12 0.0 0.0 !16 H2O2+M = OH+OH+M 1.2E17 0.0 190.5 !17 H2O2+H = HO2 + H2 1.7E12 0.0 15.7 !18 H2O2+OH = H2O+HO2 1.0E13 0.0 7.5 !19 END

___________________________________________________________________ In the initiation reaction the chain is initiated by creating OH radicals with one free bond each. More free bonds are created than consumed in the chain-branching reaction unlike the propagation reactions where one free bond is consumed and one free bond is created. In the termination reaction two free bonds are consumed, and the chain is terminated due to a recombination of the two radicals. In the recombination reactions more energy is released by bonding two molecules than the product molecule can carry, and a third species M is required that can carry some amount of the energy. (The third species M provides the energy required to split the product back to reactants in the reverse reaction). In reaction No. 6,7,8,9 and 17, M denotes an unspecified molecule that is calculated from the sum of all species concentrations in the gas times their factor of effectiveness to carry the energy released or required. The lines below reaction 6,8 and 9 contain information of enhancement factors for molecules that differ from 1 in the mixture. It can be seen that H2O has a strong third-body

efficiency.

The oxidation mechanism of hydrogen is a part of all reaction mechanisms describing oxidation of hydrocarbons and is therefore very important.

4.1.2 Surface chemistry

An important reason for choosing Pt as wall material with a catalytic combustion property is that Platinum has been studied extensively and several detailed mechanisms have been reported in the literature (Hellsing et al., 1987; Williams et al., 1992; Warnatz et al., 1994; Rinnemo et al, 1997). The mechanism by Warnatz and co-workers shown in Table 2 was used in this work.

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Table 2. Surface Reaction Mechanism for the Oxidation of Hydrogen on Platinum

(SURFACE CHEMKIN format). Source: J. Warnatz et al., Combust. Flame, 1994.

___________________________________________________________________________ SITE /PT_SURFACE/ SDEN/2.706E-9/ ! moles/cm^2

PTs H2Os Os OHs Hs H2s O2s END REACTION KJOULES/MOLE H2 + PTs = H2s 0.05 0 0 ! 1 STICK H2s + PTs = Hs + Hs 7.5E22 0 15.6 ! 2 O2 + PTs = O2s 0.023 0 0 ! 3 STICK O2s + PTs = Os + Os 2.5E24 0 0 ! 4 Hs + Os = OHs + PTs 3.7E21 0 19.3 ! 5

Hs + OHs = H2Os + PTs 3.7E21 0 0 ! 6 OHs + OHs = H2Os + Os 3.7E24 0 100.5 ! 7 H + PTs = Hs 1.00 0 0 ! 8 STICK O + PTs = Os 1.00 0 0 ! 9 STICK H2O + PTs = H2Os 0.75 0 0 !10 STICK OH + PTs = OHs 1.00 0 0 !11 STICK HO2 + 2PTs = OHs + Os 1.00 0 0 !12 STICK

H2O2 + 2PTs = OHs + OHs 1.00 0 0 !13 STICK

___________________________________________________________________________ In the mechanism in Table 2, Hs and Os etc denotes an adsorbed hydrogen and oxygen atom on the Platinum surface respectively, and PTs denotes a free surface site. Although the surface reactions for Hydrogen on Pt are relatively well established, there are uncertainties associated with surface chemistry (Warnatz, 1996a), and approaches to optimize and construct surface mechanisms is an important research area (Park et al, 1999b; Aghalayam et al., 2000).

To also have a boundary condition where the surface acts like a sink for active intermediates and thereby retarding the combustion, a surface mechanism was used with the purpose to adsorb radicals from the gas phase. The recombination on the surface then leads to desorption of stable products into the gas phase.

This surface mechanism shown in Table 3 was proposed in a work where the flow field was stagnant (Aghalayam et al., 1998). The site density was unknown for the recombination surface, but the actual value of the site density had no effect on the gas-phase species profiles.

Table 3. Surface Reaction Mechanism for Hydrogen on the Recombination Wall

(SURFACE CHEMKIN format). Source: P. Aghalayam et al., Combust. Theory. Modeling, 1998.

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__________________________________________________________________________ SITE /INERT/ SDEN /4.1683E-7/

H(S) O(S) OH(S) S END REACTIONS KJOULES/MOLE H + S => H(S) 1 0 0 ! 1 STICK 2H(S) => H2 + 2S 1E13 0 0 ! 2 O + S => O(S) 1 0 0 ! 3 STICK 2O(S) => O2 + 2S 1E13 0 0 ! 4 DUP OH + S => OH(S) 1 0 0 ! 5 STICK

2OH(S) => H2O + O(S) + S 1E13 0 0 ! 6 DUP

2O(S) => O2 + 2S 1E13 0 0 ! 7 DUP

HO2 + 2S => OH(S) + O(S) 1 0 0 ! 8 STICK

2OH(S) => H2O + O(S) + S 1E13 0 0 ! 9 DUP

2O(S) => O2 + 2S 1E13 0 0 ! 10 DUP

H2O2 + 2S => 2OH(S) 1 0 0 ! 11 STICK

2OH(S) => H2O + O(S) + S 1E13 0 0 ! 12 DUP

2O(S) => O2 + 2S 1E13 0 0 ! 13 DUP

___________________________________________________________________________

Of the assumptions used in SURFACE CHEMKIN can be mentioned:

- The adsorbates are assumed to be randomly distributed on the surface (mean field approximation)

- The surface is viewed as being uniform, the local environment is not taken into account (edges, defects, terraces, different structures).

The mechanisms shown in Table 1-3 are in CHEMKIN and SURFACE CHEMKIN format. First there is information about which elements and species that are included in the reaction mechanism and for the surface is also specified the site density in moles/cm2. DUP means that it is a duplicate reaction and STICK means that the rate constant for the reaction is formulated as a sticking coefficient. Sticking coefficients provide a means to estimate some surface reaction rates. The sticking coefficient γ (values in the range 0 to 1) can be transformed to a usual mass-action kinetic rate constant by the expression (high values of γ)

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( )

tot n k i i fi RT_W k π γ γ 2 1 2 / 1  Γ     − = . (9)

HereR= universal gas constant (J/mole⋅K), W_k= gas-phase species molecular weight (g/mole), Γtot= total site density (moles/cm2) and n is the sum of all stoichiometric

coefficients of reactants that are surface species. The square root expression is connected to the gas-surface collision frequency.

As a third boundary condition a totally inert wall was used with no species and reactions.

4.2 Conditions for the CRESLAF calculations

In the calculations an axisymmtric planar channel was considered, with the height 1 cm from the symmetry line in the middle of the channel. The pressure was atmospheric and two lean fuel-air ratios (φ) of 0.5 and 0.1 were used. The inlet temperature was 975K (simulating an ignition source) and the inlet velocity was 900 cm/s, which gave a clear shape of the reaction zone after ignition of the fuel-air mixture. Flat profiles for velocity, temperature and species were used at the inlet. The inlet boundary layer thickness was 0.01 cm (within which the velocity profile was parabolic, i.e. fully developed). The boundary layer then develops very fast downstream the channel and the velocity profile remains roughly parabolic but due to expansion of the gas the maximum velocity increases. Wall temperatures used was 600 and 400 K. The wall temperature was set equal to the gas-phase temperature at the inlet to the channel and was then linearly ramped down to the wall temperature at x = 0.5 cm. This had the consequence, that in part of the reaction zone the wall temperature varied. To elucidate the effects of mass and heat transfer the carrier gas N2 was substituted with modified Helium

(Helium with the same heat capacity as N2), see Table 1. This enhances mass- and heat

transfer rates due to the higher diffusivity and heat conductivity in modified He compared to Nitrogen. The mesh consisted of 70 points in the radial direction with the mesh points concentrated near the wall. The mesh in the axial direction is adaptive. A typical CPU-time needed for a calculation was approximately 3 1/2 min.

4.3 Results and Discussion

In Fig 2-9 are shown contour plots of the atomic hydrogen concentration, hydrogen concentration, temperature and velocity for the two fuel-air ratios at the wall temperature 600 K for all combinations of the three wall materials (denoted Pt, Rr, In) and the two carrier gases Nitrogen and modified Helium (denoted N2 and He). In the plots, y denotes the height above the symmetry line (y = 0 cm in the middle of the channel and y = 1 cm at the wall).

0 7 0 . 8 0 . 9 1 0 . 0 3 3 6 0 . 0 2 8 8 0 . 0 0 4 7 9 0 . 0 0 9 5 9 P t N 2 he ig ht y, cm 0 7 0 . 8 0 . 9 1 0 . 0 3 2 4 0 . 0 0 4 6 2 0 . 0 0 9 2 5 0 . 0 0 4 6 2 P t H e

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Fig. 2. Contour of the H-atom concentration (mole fractions), φ = 0.5, TW = 600K.

Chemical species concentrations result from gas-phase chemical reactions in the fluid-flow field. Because the reactions are very temperature sensitive, they exhibit a two-dimensional variation with the gas-phase temperature. The resulting concentration fields are thus a sensitive function of wall temperature, flow velocity and carrier gas. The hydrogen atom concentration is a measure of the overall combustion rate and therefore indicates the shape and position of the reaction zone. The diagrams for the inert wall material (InN2 and InHe) give information on the extent of the wall effects due to heat transfer combined with the effect of no slip at the wall, and the development of the boundary layer compared to a free flame.

0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 0 . 0 0 2 0 . 0 0 1 3 3 0 . 0 0 0 6 6 7 0 . 0 0 0 2 2 2 P t N 2 hei gh t y , cm 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 0 . 0 0 1 8 8 0 . 0 0 0 2 0 9 0 . 0 0 1 2 5 P t H e 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 0 . 0 0 1 7 7 0 . 0 0 2 0 . 0 0 0 2 2 2 0 . 0 0 0 6 6 5 R rN 2 hei ght y , cm 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 0 . 0 0 1 8 4 0 . 0 0 1 8 4 0 . 0 0 0 2 0 4 R rH e 0 7 0 . 8 0 . 9 1 0 . 0 0 2 0 2 0 . 0 0 0 4 4 9 0 . 0 0 0 2 2 5 In N 2 he ig ht y , cm 0 7 0 . 8 0 . 9 1 0 . 0 0 2 0 . 0 0 1 5 5 0 . 0 0 0 2 2 2 In H e

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Fig. 3 Contour of the H-atom concentration (mole fractions), φ = 0.1, TW = 600K.

There is a large part of the channel where the reaction rate is totally unaffected by the wall. The size of this central part of the channel is apparent from the contour plots. For example according Fig. 2 the H-atom concentration profiles within the reaction zone are flat at about ca 8 mm from the middle of the channel, while they are affected by the wall in an area within 2 mm from the wall.

Fig. 4. Contour of the H2 concentration (mole fractions), φ = 0.5, TW = 600K.

In a large central portion of the channel, the velocity profile is flat. In the reaction zone in this part of the channel, the concentrations and temperature profiles also are flat without any influence from the wall. In this section the reaction rate is constant perpendicular to the flow due to the equalizing effect of diffusion and heat conduction in that direction. The central part is not interesting in this context; the attention is given to the boundary layer at the wall where velocity, temperature and concentrations strongly vary with the distance from the wall. The contour plots are emphasizing the boundary layers within the reaction zone and show a section of the channel that includes a distance of 2-3 mm outward from the wall and an axial distance of 3-6 mm around the reaction zone.

0 . 1 0 . 2 0 . 3 0 . 4 0 . 8 0 . 9 1 0 . 1 6 0 . 1 4 0 . 1 2 0 . 1 0 . 0 2 P t N 2 he ig ht y, cm 0 . 1 0 . 2 0 . 3 0 . 4 0 . 8 0 . 9 1 0 . 1 6 0 . 1 4 0 . 1 0 . 0 8 0 . 0 2 P t H e 0 . 1 0 . 2 0 . 3 0 . 4 0 . 8 0 . 9 1 0 . 1 6 0 . 1 4 0 . 1 2 0 . 0 2 R rN 2 he ig ht y , cm 0 . 1 0 . 2 0 . 3 0 . 4 0 . 8 0 . 9 1 0 . 1 6 0 . 1 4 0 . 1 0 . 0 2 R rH e 0 . 1 0 . 2 0 . 3 0 . 4 0 . 8 0 . 9 1 0 . 1 6 0 . 1 4 0 . 1 2 0 . 0 4 In N 2 hei ght y , c m d is t a n c e x , c m 0 . 1 0 . 2 0 . 3 0 . 4 0 . 8 0 . 9 1 0 . 1 6 0 . 1 4 0 . 1 0 . 0 2 In H e d is t a n c e x , c m

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Fig. 5 Contour of the H2 concentration (mole fractions), φ = 0.1, TW = 600 K.

For φ=0.5 the wall effects at inert walls are fairly small, especially the effect on the H2

-conversion (see Fig. 4). When the wall material is changed to a material that gives recombination of radicals, there is a decrease of the H concentration close to the wall. The effect of the wall is seen more far from the wall than in the case of an inert wall material. The H concentration at the wall and in a zone close to the wall becomes almost equal to zero (see Fig. 2). The effect on H2-conversion is still small but significant (see Fig. 4).

However, the general structure of the reaction zone is not changed. With a Pt-wall an even lower H concentration compared with the recombination wall and the inert wall is obtained. Here the depletion of H radicals close to the wall is unexpectedly more pronounced than with the recombination surface (see Fig. 2).

0 . 4 0 . 6 0 . 8 1 0 . 8 0 . 9 1 0 . 0 0 4 0 4 0 . 0 1 6 1 0 . 0 3 2 1 0 . 0 3 6 1 P t N 2 hei gh t y , cm 0 . 4 0 . 6 0 . 8 1 0 . 8 0 . 9 1 0 . 0 0 4 0 5 0 . 0 1 2 1 0 . 0 2 4 1 0 . 0 3 2 2 0 . 0 3 6 2 P t H e 0 . 4 0 . 6 0 . 8 1 0 . 8 0 . 9 1 0 . 0 0 4 0 8 0 . 0 0 8 1 3 0 . 0 2 0 3 0 . 0 3 6 5 R rN 2 hei ght y , cm 0 . 4 0 . 6 0 . 8 1 0 . 8 0 . 9 1 0 . 0 0 4 0 8 0 . 0 1 2 2 0 . 0 2 4 3 0 . 0 3 2 4 0 . 0 3 6 4 R rH e 0 . 4 0 . 6 0 . 8 1 0 . 8 0 . 9 1 0 . 0 0 4 0 8 0 . 0 0 8 1 2 0 . 0 1 2 2 0 . 0 3 6 4 In N 2 he ig ht y , cm d is t a n c e x , c m 0 . 4 0 . 6 0 . 8 1 0 . 8 0 . 9 1 0 . 0 0 4 0 7 0 . 0 1 2 2 0 . 0 2 8 3 0 . 0 3 6 4 In H e d is t a n c e x , c m 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 9 e + 0 0 3 1 . 7 1 e + 0 0 3 9 7 1 1 . 3 4 e + 0 0 3 P t N 2 he ig ht y , cm 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 9 e + 0 0 3 1 . 7 1 e + 0 0 3 9 7 1 1 . 1 6 e + 0 0 3 P t H e 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 9 e + 0 0 3 1 . 7 2 e + 0 0 3 9 7 2 R rN 2 he ig ht y , c m 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 9 e + 0 0 3 1 . 7 1 e + 0 0 3 7 8 5 9 7 0 R rH e 0 . 8 0 . 9 1 1 . 9 e + 0 0 3 1 . 7 1 e + 0 0 3 9 7 1 In N 2 he ig ht y , cm 0 . 8 0 . 9 1 1 . 9 e + 0 0 3 1 . 7 1 e + 0 0 3 9 7 0 In H e

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Fig. 6 Contour of the temperature (K), φ = 0.5, TW = 600 K.

The more pronounced depletion of H-radicals in case of a Pt wall compared to a recombination wall may be due to three causes. The first one is the net adsorption of H-radicals on the wall being higher for Pt than for the recombination wall. The second one is the depletion of hydrogen in the boundary layer due to catalytic combustion on Pt resulting into lower production of H-radicals in this layer. The third one is increased H-radical depletion in the boundary layer due the third body effect caused by high water concentration in this layer (see reactions No. 6 and 9 in Table 1). This high concentration is due to the production of water by the catalytic combustion on the Pt wall. The latter type of product inhibition was also found in stagnation point flow geometry, where the homogeneous ignition of H2 was

inhibited by catalytic formation of H2O (Vlachos, 1996; Bui et al., 1996).

Fig. 7 Contour of the temperature (K), φ = 0.1, TW = 600 K.

Fig. 2 showing the H-concentrations suggests the third cause, that is, increased H-radical recombination due the third body effect of water. It cannot be the first one since H-radical adsorption is slower on Pt than on the recombination wall. This can be seen since the rate of H-radical adsorption is proportional to the H-radical concentration gradient near the wall and this gradient is much less for the Pt-wall than for the recombination wall according to the contour plots (Fig. 2). The second cause, hydrogen depletion, can be excluded by comparing the contour plots for H-radical concentration (Fig. 2) and the contour plots for hydrogen concentration (Fig. 4). This shows that the H-radical concentrations are more depleted for the Pt wall compared to the recombination wall also in parts of the boundary layer without

0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 2 e + 0 0 3 1 . 1 4 e + 0 0 3 1 . 0 7 e + 0 0 3 9 3 5 P t N 2 hei gh t y , cm 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 9 3 5 8 6 8 1 e + 0 0 3 1 . 0 7 e + 0 0 3 1 . 2 e + 0 0 3 P t H e 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 2 1 e + 0 0 3 9 3 9 1 . 0 1 e + 0 0 3 1 . 1 4 e + 0 0 3 R rN 2 hei ght y , cm 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 e + 0 0 3 1 . 0 7 e + 0 0 3 9 3 6 8 0 1 1 . 2 e + 0 0 3 R rH e 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 2 1 e + 0 0 3 1 . 1 4 e + 0 0 3 1 . 0 7 e + 0 0 3 9 3 9 In N 2 he ig ht y , cm d is t a n c e x , c m 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 2 e + 0 0 3 9 3 6 1 e + 0 0 3 1 . 0 7 e + 0 0 3 8 6 9 In H e d is t a n c e x , c m

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hydrogen depletion. This would not be the case if hydrogen depletion was the cause of the excessive H-radical depletion in case of a Pt wall. Furthermore, more unburnt hydrogen is left in case of a Pt-wall than in case of a recombination wall.

Fig. 8 Contour of the velocity (cm/s), φ = 0.5, TW = 600 K

The effect of changing the carrier gas from nitrogen to modified helium can be seen in Fig. 6 and 8. The boundary layers become thicker when helium is the carrier gas, as would be expected due to the higher heat conductivity and diffusivity of helium. But the same differences remain in the H molar concentration profile near the wall for the three wall materials when changing from N2 to modified He (see Fig. 2). This indicates that it is the

chemical interactions on the wall that give rise to most of the wall effects when φ=0.5.

When the surface temperature is decreased to 400 K, the same trends can bee seen as for the case with a wall temperature of 600 K, but the H-atom concentrations have significantly decreased. This is also in agreement with that the chemical interaction with the wall is pronounced when φ=0.5. The effect on unburned H2 on the other hand was minor when

decreasing the wall temperature.

As the fuel equivalence ratio is decreased to 0.1, the situation becomes different. A significant difference compared to the richer combustion case is found for the inert surface material (In). The H concentration has become almost zero close to the wall and the differences between the three wall materials has become small (see Fig. 3). The thermal and velocity boundary layer has become thicker compared to when φ=0.5 (see Fig. 7 and 9). This indicates that heat and momentum transport have become more important for the wall effects. InFig. 5 are shown the H2 profiles. They have become more similar for different wall materials compared to the

richer case. This means that the combustion is less affected by the reactions on the wall, and also indicates that the thermal wall effects have become more important than the chemical

0 . 2 0 . 4 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 5 9 e + 0 0 3 1 . 3 9 e + 0 0 3 1 . 1 9 e + 0 0 3 7 9 6 P t N 2 he ig ht y , cm 0 . 2 0 . 4 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 6 e + 0 0 3 1 . 4 e + 0 0 3 1 . 2 e + 0 0 3 8 0 2 P t H e 0 . 2 0 . 4 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 6 e + 0 0 3 1 . 4 e + 0 0 3 1 . 2 e + 0 0 3 8 0 1 R rN 2 he ig ht y , c m 0 . 2 0 . 4 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 6 2 e + 0 0 3 1 . 4 1 e + 0 0 3 1 . 2 1 e + 0 0 3 8 0 8 6 0 6 R rH e 0 . 2 0 . 4 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 6 1 e + 0 0 3 1 . 4 1 e + 0 0 3 1 . 2 1 e + 0 0 3 8 0 4 In N 2 he ig ht y , cm d is t a n c e x , c m 0 . 2 0 . 4 0 . 6 0 . 7 0 . 8 0 . 9 1 1 . 6 2 e + 0 0 3 1 . 4 1 e + 0 0 3 1 . 2 1 e + 0 0 3 8 0 8 In H e d is t a n c e x , c m

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wall effects. That is, the thermal coupling between the flame and the wall is stronger when leaner mixtures are burned. Consequently, a pronounced increase of unburnt H2 in the

boundary layer resulted when the wall temperature was decreased from 600 K to 400 K. However, the effect on H-atom concentrations was minor. In Fig. 5 with the H2-profiles it can

also be seen that the overall effects from the wall are more pronounced (i.e. a lower conversion) at φ=0.1 than at φ=0.5. This is as would be expected. A lower concentration of fuel near the wall gives a lower reaction rate and therefore is more easily affected by disturbances from the wall. And these wall effects are mainly thermal.

Fig. 9 Contour of the velocity (cm/s), φ = 0.1, TW = 600 K

0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 0 6 e + 0 0 3 9 4 3 7 0 8 P t N 2 he ig ht y, cm 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 0 8 e + 0 0 3 9 5 8 7 1 8 P t H e 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 0 6 e + 0 0 3 9 4 4 7 0 8 R rN 2 hei ght y , c m 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 0 8 e + 0 0 3 9 5 9 7 1 9 R rH e 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 0 6 e + 0 0 3 9 4 3 7 0 7 In N 2 hei ght y , c m d is t a n c e x , c m 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 7 0 . 8 0 . 9 1 1 . 0 8 e + 0 0 3 9 5 9 7 1 9 In H e d is t a n c e x , c m

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5 Methane as model fuel (II)

In the second investigation the model fuel was methane. Methane is a major constituent in natural gas and the simplest of the hydrocarbons. It is an important model fuel both for automotive- and gas turbine applications. In turbines the wall temperatures used are much higher than in internal combustion engines, and the wall effects can also be expected to be different. It should be noted that although methane is a hydrocarbon, the burning characteristics is not typical for hydrocarbons. The results obtained may therefore not be true for higher hydrocarbons like propane and butane.

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Previous numerical investigations on wall effects with methane as model fuel had primarily used the one-dimensional stagnation point flow and isothermal inert walls (for example Vlachos, Schmidt and Aris 1994a; 1994b; Popp and Baum, 1997). It was shown that the if the wall removes reactive intermediates, it strongly affects homogeneous ignition and extinction, and that the composition of species in combustion near surfaces can deviate significantly from freely propagating flames, and is determined by a combination of kinetic and transport effects. For stoichiometric laminar methane flames stagnating on inert isothermal walls, the surface can no longer be modelled as chemically inert above wall temperatures of 400 K, and surface recombination reactions especially for H and OH have to be described at 600 K (Popp et al., 1996). The sidewall flow, however, is not used frequently in the numerical modeling work of flame-wall interaction. This geometry is important and quench in an engine under practical conditions occurs during turbulent shear flow and not under laminar head-on flow conditions (Kiehne et al., 1986). The sidewall configuration is also the most interesting in gas turbines. Therefore, the aim of this study was to investigate the wall effects of stationary CH4

flames with CRESLAF in a two-dimensional sidewall configuration, and especially the thermal and kinetic effects the cooled wall gave rise to.

5.1 Chemical Kinetic Models

5.1.1 Gas phase chemistry

The gas-phase chemistry describing methane oxidation in air is quite complex and contains hundreds of reactions. In this work was used the Gas Research Institute-mechanism version 1.2 with it’s corresponding thermodynamic and transport databases (Frenklach et el., 1995). This mechanism has been optimized at lean-to-stoichiometric fuel mixtures, over a wide range of pressures and residence times, and represents of the most recent and comprehensive methane oxidation reaction mechanisms. There are two parallel oxidation paths in the methane system: one via the oxidation of methyl radicals and the other via the oxidation of ethane. For fuel lean mixtures the former path dominates and therefore only this path (also known as the C1-path) was considered here. Consequently, the reaction ⋅ CH3 + ⋅ CH3 + M =

C2H6 + M and all third body efficiencies for C2H6 was removed from the reaction mechanism.

The ethane oxidation path is also known as the C2-path of the methane oxidation. The reduced

mechanism had 23 species (including the carrier N2) among 119 reversible reactions.

Including only the C1-path has the advantage that the CPU-time needed for the calculations is

reduced.

5.1.2 Surface chemistry

To describe the interaction of the flame with the wall, two different surface mechanisms were used in the simulations: one on platinum and the other one on an inert wall promoting radical recombination; the same type of boundary conditions that were used for hydrogen as model fuel.

The recombination mechanism was the same as in Table 3. Removing the radicals H, OH and O will also retard the methane oxidation in the boundary layer, as they are important chain

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carriers. The surface chemistry of methane is more complex than it is for hydrogen. For example the catalytic oxidation of methane on Pt must in addition to methane also include the surface reactions of carbon monoxide and hydrogen. The surface mechanism for CH4 on Pt is

therefore generally not as well understood compared to hydrogen. In recent years work has been carried out to find the rate coefficients of the elementary reactions of methane oxidation on platinum (Deutschmann et al, 1996; Aghalayam et al, 2001; Chou et al., 2000). In this work the mechanism by Deutschmann et al. 1996 was used. The reaction steps are shown in Table 4. For details of the rate constants, see the source.

Table 4. Surface Reaction Scheme for Methane Oxidation on Platinum

Source: O. Deutschmann, et al., Proc. Twenty-Sixth Symposium (International) on

Combustion, 1996. __________________________________________________________________________ Adsorption: CH4 + 2PT(S) => CH3(S) + H(S) H2 + 2PT(S) => 2H(S) H + PT(S) => H(S) O2 + 2PT(S) => 2O(S) O + PT(S) => O(S) H2O + PT(S) => H2O(S) CO + PT(S) => CO(S) OH + PT(S) => OH(S) Surface Reactions: C(S) + O(S) => CO(S) + PT(S) CO(S) + PT(S) => C(S) + O(S) CH3(S) + PT(S) => CH2(S) + H(S) CH2(S)s + PT(S) => CH(S) + H(S) CH(S) + PT(S) => C(S) + H(S) CO(S) + O(S) => CO2(S) + PT(S)

H(S) + O(S) = OH(S) + PT(S) H(S) + OH(S) = H2O(S) + PT(S) OH(S) + OH(S) = H2O(S) + O(S) Desorption: 2H(S) => H2 + 2PT(S) 2O(S) => O2 + 2PT(S) H2O(S) => H2O + PT(S) OH(S) => OH + PT(S) CO(S) => CO + PT(S) CO2(S) => CO2 + PT(S) ______________________________________________________________ 5.2 Conditions for the CRESLAF calculations

The conditions for the calculations were slightly changed compared to when hydrogen was model fuel. The channel was axisymmetric in planar coordinates, but the height was decreased to 0.5 cm from the symmetry line in the middle of the channel. A narrower channel will make the effect of heterogeneous reactions more significant. Two lean fuel-air ratios (φ) of 0.4 and 0.2 were used, and the inlet velocity was 200 cm/s. The validity of the boundary layer equations as compared to an elliptic approach (where axial diffusion terms are included)

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depends strongly on the inlet velocity and the fuel-air ratio (Mantzaras et al., 2001). See also section 6 on this topic. The inlet temperature was 1200 K (simulating an ignition source). A higher inlet temperature was needed for methane than for hydrogen to cause ignition. Wall temperatures used was 600 and 1200 K and the wall was isothermal. To elucidate the influence of pressure on the wall effects, in addition to atmospheric pressure also a pressure of 10 atmospheres was used. This will increase the concentration, but also enhance the rate of third-body reactions in the gas-phase in favour of bimolecular reactions.

The mesh consisted of 70 points in the radial direction with the mesh points concentrated near the wall. A typical CPU-time needed for a calculation was approximately 20 min.

5.3 Results and Discussion

Like in the study with hydrogen the same type of boundary conditions were used: A wall (Pt) that causes catalytic combustion of methane, a wall that causes free radicals to recombine on the surface and produce stable species (Rec), and a completely chemically inert wall (In). The reason for choosing these walls was to estimate the importance of the chemical wall effects compared to the thermal wall effects when changing the fuel-air ratio, wall temperature and pressure. Also comparing with the results obtained for hydrogen is important, as some wall effects may be fuel-independent.

In Fig. 10 is shown a contour of the CH4 concentration (mole fractions) at φ = 0.4. The

centerline of the channel is at the radial position 0 cm and the wall is at the radial position 0.5 cm. The left column corresponds to the wall temperature 600 K and the right column to the wall temperature 1200 K. For the lower wall temperature (600K) the effect on the CH4

conversion when changing the wall material is fairly small. The reaction kinetics on the catalytic wall is limited by the availability of free surface sites and the surface is covered by adsorbed atomic oxygen (O(S)). In addition, the shape of the H-atom concentration profiles is the same for the three wall materials and the concentration is almost zero close to the wall.

When the wall temperature is increased to 1200 K the situation changes. The reaction rate and conversion of CH4 has increased. The reactions at the Pt wall (Pt) have ignited but the

homogeneous conversion of methane is retarded to a small extent near the wall compared to the inert wall (In) but not as much as the recombination wall (Rec). For the Pt-wall the H-atoms are depleted close to the wall in comparison with the recombination wall (Rec) and the inert wall.

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28 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.039 0.02 0.0001 Pt ra d. d is t., cm 0 0.5 1 1.5 2 2.5 0 0.2 0.4 Rec ra d. d is t., c m 0 0.5 1 1.5 2 2.5 0 0.2 0.4 In ra d. d is t., c m axial dist., cm 0 0.5 1 1.5 0 0.2 0.4 0.039 0.02 0.0001 Pt 0 0.5 1 1.5 0 0.2 0.4 Rec 0 0.5 1 1.5 0 0.2 0.4 In axial dist., cm

Fig. 10 Contour of the CH4 concentration (mole fractions), φ = 0.4, p = 1 atm.

As fuel air-ratio is decreased to 0.2 the same observations between the three wall materials can be seen at the lower wall temperature as for φ=0.4, but the reaction zone has become thicker and the thermal coupling between the flame and the wall is more pronounced compared to the richer mixture. Due to the lower temperature developed by the homogeneous reactions the fuel conversion is more retarded close to the cold wall. At the higher wall temperature the Pt wall (Pt) promotes the conversion of methane in the middle of the channel but retards the conversion close to the wall when compared to the inert wall (In). The conversion is still better for the Pt-wall compared to the recombination wall. As for the richer mixture the H-atom concentration has become almost zero close to the Pt-wall compared to the other wall materials.

In Fig 11 is shown the temperature profiles for the Pt-wall at 1200 K and 1 atm. For both fuel-air ratios the reactions have completed before the thermal boundary layer is fully developed.

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29 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 1210 1400 1600 1800 2000 2020 (c) axial dist., cm ra d. d is t., c m 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1210 1400 1600 1800 2000 2040 (d) axial dist., cm 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1210 1300 1400 1500 1600 1620 (b) 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 1210 1300 1400 1500 1600 1620 (a) ra d. di st , c m

Fig. 11 Contour of the temperature (K) for the Pt-wall at TW = 1200 K;

(a) φ = 0.2, p = 1 atm, (b) φ = 0.2, p = 10 atm, (c) φ = 0.4, p = 1 atm, (d) φ = 0.4, p = 10 atm.

When increasing the pressure to 10 atm the inlet concentration is increased. This means that the reaction rate is much higher and the reaction zone is moved towards the inlet of the channel. Also, the reaction zone is much thinner than at 1 atm due to the higher concentration and mass-burning rate. Approximately one tenth of the boundary layer is developed when the reactions are complete (see Figure 11).

For the lower wall temperature and φ=0.4 the conversion of CH4 and the shape of the H-atom

profiles are not affected by the wall material, the same result as for atmospheric pressure (see Fig. 12-13, left column). But at the higher wall temperature the Pt wall now retards the conversion close to the wall more than the recombination wall (see Fig. 12, right column). The explanation for this behaviour follows: A higher pressure leads to increased concentration and more production of H2O by catalytic conversion. But the higher pressure

also leads to diffusion limitations. This leads to a high water concentration in the boundary layer leading to a decrease in the H-atom concentration when water acts like a third body in reactions 6 and 9 in Table 1 (see Fig 13, right column).

Thus hydrogen atoms are transformed into the much less active hydroperoxyl radicals or water molecules leading to inhibition of the conversion of methane for the Pt-wall compared

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to the other wall materials. In an experimental and theoretical study on of the effect of thermal barriers and catalytic coatings in a Homogeneous Charge Compression Ignition (HCCI) engine, the catalytic coatings proved to have a negative effect on unburned hydrocarbon emissions through catalytic flame quenching (Hultqvist et al., 2000). Of the model fuels used were natural gas and iso-octane (i-C8H18) and the pressure was elevated. This supports the

findings in this work: At higher wall temperatures and pressures the catalytic wall retards the homogeneous combustion of methane due to the water produced by catalytic combustion.

0 0.1 0.2 0.3 0.4 0.4 0.45 0.5 0.039 0.02 0.001 Pt ra d. d ist , cm 0 0.1 0.2 0.3 0.4 0.4 0.45 0.5 Rec ra d. d is t., c m 0 0.1 0.2 0.3 0.4 0.4 0.45 0.5 In axial dist., cm ra d. d is t., c m 0 0.05 0.1 0.15 0.2 0.4 0.45 0.5 0.039 0.02 0.001 Pt 0 0.05 0.1 0.15 0.2 0.4 0.45 0.5 Rec 0 0.05 0.1 0.15 0.2 0.4 0.45 0.5 In axial dist., cm

Fig. 12 Contour of the CH4 concentration (mole fraction), φ = 0.4, p = 10 atm.

When the fuel-air ratio is decreased to 0.2 the thermal effects dominate at the lower wall temperature as expected, and are more pronounced than for the richer mixture. At the higher wall temperature, for the Pt-wall the same significant product inhibition effect as for the richer mixture is observed (see Fig. 14).

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31 0 0.1 0.2 0.3 0.4 0.45 0.5 1e-5 1e-4 2e-4 Pt ra d. d is t., cm 0 0.1 0.2 0.3 0.4 0.45 0.5 Rec ra d. d is t., c m 0 0.1 0.2 0.3 0.4 0.45 0.5 In ra d. d is t., c m axial dist., cm 0 0.05 0.1 0.15 0.2 0.4 0.45 0.5 1e-5 1e-4 2e-4 Pt 0 0.05 0.1 0.15 0.2 0.4 0.45 0.5 Rec 0 0.05 0.1 0.15 0.2 0.4 0.45 0.5 In axial dist., cm

Fig. 13 Contour of the H atom concentration (mole fractions), φ = 0.4, p = 10 atm.

0 0.5 1 0.4 0.45 0.5 0.02 0.01 0.0005 Pt ra d. d is t., cm 0 0.5 1 0.4 0.45 0.5 Rec ra d. d is t., c m 0 0.5 1 0.4 0.45 0.5 In axial dist., cm ra d. d is t., c m 0 0.1 0.2 0.4 0.45 0.5 0.02 _0.01 0.0005 Pt 0 0.1 0.2 0.4 0.45 0.5 Rec 0 0.1 0.2 0.4 0.45 0.5 In axial dist., cm

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6 The validity of the boundary layer assumption

Richer fuel/air mixtures have a larger axial diffusion component than leaner mixtures. This will lead to a considerable contribution of upstream propagation of the flame stabilization process. The last aspect is suppressed in the boundary layer assumption, i.e the axial diffusion is neglected to the convective transport in the principal flow direction (∂/∂x<<∂/∂y). Elliptic computations, where the axial diffusion terms are included, yield shorter ignition distances compared to computations relying on the boundary layer assumption (i.e. CRESLAF). However, the computational work is one order in magnitude higher for elliptic computations compared to using the boundary layer assumption. As φ decreases the discrepancy diminishes between the elliptic and parabolic approach. The key parameters determining the agreement between the two types of computations is φ and the inlet velocity (Mantzaras et al., 2001). At higher pressures the laminar flame speed is reduced (Glassman, 1996b), making the boundary layer equations more accurate at lower inlet velocities. The laminar flame speed is the velocity at which unburned gases move through the combustion wave in the direction normal to the wave surface.

In this work fuel-air ratios less than or equal 0.5 have been used. To estimate the discrepancy in flame position when neglecting the axial diffusion in the boundary layer approach, calculations were performed with PREMIX (Kee et al., 1985), another part of the CHEMKIN-collection. With PREMIX, where axial diffusion is considered, steady, laminar, one-dimensional premixed flames can be modeled.

In Fig. 15-20 is shown the axial position of the burner-stabilized flame calculated with PREMIX with the same initial conditions as in the boundary layer calculations. When the position of the reaction zone is compared with the results from boundary layer calculations it can be seen that for the leaner combustion cases (φ=0.2 and 0.1) has as expected the axial diffusion small impact on the position of the reaction zone except for hydrogen at atmospheric pressure. This is due to the fact that hydrogen has a very high mass diffusivity. But already at an inlet velocity of 9.5 m/s instead of 9 m/s, the flame was pushed away from the inlet making axial diffusion less important.

For the richer combustion cases (φ = 0.4 and 0.5) on the other hand there is a significant difference at atmospheric pressure but not at the higher pressure (methane). Here the laminar flame speed is significantly reduced making the discrepancies small. To possibly overcome the discrepancy at atmospheric pressure, the inlet velocity should be higher to make the difference smaller.

Note that the discrepancy between the PREMIX and the CRESLAF calculations for the richer combustion cases at one atmosphere does not necessarily mean that consideration of axial diffusion would change the position of the flame in the boundary layer significantly. It is a question that not has been able to be answered. In the other cases the agreement between the two calculations strongly suggests that the axial diffusion may be safely neglected.

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34 φ = 0.5, p=1atm, H2/air 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,00 0,10 0,20 0,30 0,40 0,50 distance, cm mole fractions H2 H2O H*10

Fig. 15 Calculations with PREMIX. H2/air, φ = 0.5, p = 1atm, TIN = 975 K, UIN = 9 m/s.

φ=0.1, p=1 atm, H2/air 0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,00 0,10 0,20 0,30 0,40 0,50 distance, cm mole fractions H2 H2O H*30

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35 0,000 0,010 0,020 0,030 0,040 0,050 0,060 0,070 0,080 0,090 0,00 0,05 0,10 0,15 0,20 0,25 0,30 distance, cm mole fractions H2O CO2 CO CH4 H*50 φ = 0.4, p = 1 atm

Fig. 17 Calculations with PREMIX. CH4/air, φ = 0.4, p = 1 atm, TIN = 1200 K, UIN = 2 m/s.

0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,00 0,05 0,10 0,15 0,20 0,25 distance, cm mole fractions CH4 H2O CO2 H*100 φ = 0.4, p = 10 atm

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36 0,000 0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040 0,045 0,050 0,00 0,50 1,00 1,50 2,00 distance, cm mole fractions CH4 H2O CO2 H*100 φ = 0.2, p = 1 atm

0,000 0,010 0,020 0,030 0,040 0,050 0,00 0,05 0,10 0,15 0,20 0,25 distance, cm mole fractions CO2 H2O CH4 H*500 φ = 0.2, p = 10 atm

Numerical Studies of Wall Effects of Laminar Flames